Yes! AVG free version 7.5 & above will work fine with 64 bit OS.
AVG 9.0 Should work fine with Windows 7 64 bit.
My personal opinion!
Throw away AVG free. Go with Avira Antivir (Free only)
Download & Install the following 3 freewares. It forms a free complete security suite for your system!
1. Avira Anvivir - http://www.free-av.com/en/download/index.html
Avira is best & light solution for excellent overall system protection & internet security with real time updates, .
2. Malwarebytes - http://www.malwarebytes.org/
Malwarebytes is one of the best & effective antimalware tool out there.
3. Ccleaner - http://www.piriform.com/ccleaner/download
CCleaner is a system optimization, privacy and cleaning tool with an efficient & most useful registry cleaner.
The Best Security & System Optimization combo for all types of systems.